{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.mlab as mlab\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import random\n",
    "import time\n",
    "num_add_1 = 0\n",
    "lst_num = []\n",
    "for x in range(1000):\n",
    "    num = random.expovariate(0.11)\n",
    "    lst_num.append(num)\n",
    "    num_add_1 = num + num_add_1\n",
    "    m, s = divmod(num_add_1, 60)\n",
    "    h, m = divmod(m, 60)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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A5R3ZOb7uEbbCyWNH1z0CAABsFXcwAwAAAAAwIjADAAAA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\nAIC1CJgBAAAAAFjLn523ja+fNiB+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107740400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "num_bins = 50\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(20,16))\n",
    "\n",
    "# the histogram of the data\n",
    "n, bins, patches = ax.hist(lst_num, num_bins, normed=1)\n",
    "# add a 'best fit' line\n",
    "ax.set_xlabel('Smarts')\n",
    "ax.set_ylabel('Probability density')\n",
    "ax.set_title(r'Histogram of IQ: $\\mu=9.187$, $\\sigma=0.11$')\n",
    "\n",
    "# Tweak spacing to prevent clipping of ylabel\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "speed_arrival = 0.11\n",
    "speed_service = 0.089"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import stats "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x9554748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.arange(0,1000)\n",
    "y = stats.poisson.pmf(n, 396)*396\n",
    "plt.plot(n, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qwKkDmlc+z+korkdxBSCnPLTnIQW9QQorYJKW1y1nb8wEUVwByCkb921UwMeq6cBkhLwh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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x826dcc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_arrival = stats.poisson.rvs(0.11, loc=0, size = 3600)\n",
    "data_service = stats.poisson.rvs(0.077, loc = 0, size = 3600 )\n",
    "cumsum_arrival = data_arrival.cumsum()\n",
    "cumsum_service = data_service.cumsum()\n",
    "line = np.arange(0,3600)\n",
    "fig, ax = plt.subplots(figsize = (10,5))\n",
    "plt.plot(line, cumsum_arrival, 'g', lw = 1)\n",
    "plt.plot(line,cumsum_service, 'w')\n",
    "plt.xlim(0, 500)\n",
    "plt.ylim(0, 60)\n",
    "ax.spines['top'].set_visible(False)\n",
    "ax.spines['right'].set_visible(False)\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.fill_between(line, cumsum_arrival, cumsum_service, color = 'g', alpha = 0.8)\n",
    "ax.fill_between(line, cumsum_service, 0,  color = 'w', alpha = 1.2)\n",
    "plt.savefig(r\"D:\\picture\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Histogram of IQ: $\\\\mu=9.187$, $\\\\sigma=0.11$'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r'Histogram of IQ: $\\mu=9.187$, $\\sigma=0.11$'"
   ]
  }
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